Graphical Zoo

The Grammar of Graphics

English grammar (and that of other languages) is often used to identify which structures are correct and which incorrect. This is a normative or prescriptive use. For instance, here is a correct sentence:

“Amy gave Bill a pen.”

And here is a another expression that uses many of the same words:

“Pen Bill Amy a.”

The first is comprehensible; a real sentence. It follows the rules of English grammar for a sentence. This one has a noun, a verb, a direct and indirect object. The second does not: it is just a set of words.

There’s another use for grammar: to identify the roles of different words or phrases and help in the construction of complex expressions. You can use grammar to take a sentence apart — noun, verb, object — and then create more complex or detailed sentences by substituting new expressions for the old ones. “Amy gave Bill a pen,” might be restyled, “The girl from the soccer team ended up handing over the red ballpoint to her friend.”

A grammar of graphics has been proposed [Wilkinson, L. (2005),The Grammar of Graphics(2nd ed.). Statistics and Computing, New York: Springer] that enables graphics to be taken apart and put together. One use for such a grammar is to enable people to describe the graphics they want so that computer can do the drawing. The description has to be precise and unambiguous. The use of grammar to define the interface between people and computers is important, [Wickham, A layered grammar of graphics.] particularly for software designers [Ref: ggplot2]

A grammar is also useful for the purpose of designing and thinking about graphics. Among other things, it allows the designer to identify broad types of the components of graphics and to consider how to replace a given form of a component for one that might be better suited for the purpose at hand. Taking apart the sentence, “Amy gave Bill a pen,” allows you to think about how you might make the sentence more effective for your purpose. Noun, verb, indirect object, direct object. So “Amy” can be replaced with “The girl from the soccer team,” or “the teacher,” or “the sales clerk,” among the infinity of possibilities. All of the possibilities play the role of a noun; some of them might accurately describe the situation. Similarly, you might replace the verb (past tense) “gave” with another form of verb phrase that can take a direct and indirect object: “handed,” “will present”, “had given”, “will have had given,” etc.

Once you know that “Amy” is a noun, you can think about what other noun phrases might be more appropriate. The grammar allows you to avoid limiting yourself. For instance, a noun doesn’t have to be a person: “The dispenser gave Bill a pen.”

Usually when describing data-driven graphics [[is that a good name, data-driven]], people resort to naming the objects — scatter plot, histogram, bar plot, pie chart, maps, etc. — and describing the quantities or categories to be rendered: make a scatter plot of weight versus age.

As you’ll see, it can help to have more general categories. The categories and components to be used here may seem at first to be abstract and counter-intuitive. For instance, scatterplots, bar plots, pie charts and maps are all different forms of the same kind of entity, even though they look very different.